Wifi transmission happens in two frequencies - 2.4 GHz and 5 GHz channels. Till around a decade before, 802.11b Wi-Fi routers used to operate on the 2.4GHz band and were used in a home setting. 802.11a (5 GHz) was used in commercial settings.
With the advent of 802.11n, Wifi routers began supporting dual bands, that is both 2.4 GHz and 5 GHz channels as a standard feature.
1. Greater flexibility since you don't have to worry about in which setting the router is going to work. You might have some old devices at home with work only in the 2.4 GHz channel, so with these routers, both your old and new devices work.
2. 5 GHz channel offers greater bandwidth, a dual-band router enables your devices to take advantage of this.
In short, you need to see if you have any old device like a Microwave Over which connects through Wifi for wireless control or a Cordless phone, you need a dual band router surely to support these old as well as your new devices including your laptop and smartphone. Nowadays, most routers are dual-band only so the one you are using, unless it is a decade old, it will be working on dual-band.